Definite Integral

Question

Integration from 0 to infinity x2 / (xsinx ecosx)2

Rinkoo Gupta · Accepted Answer

integral lim x=0 to infinity x^2/x^2sin^2xe^2cos^2x

=integral lim x=0 to infinity 1/sin^2xe^2cos^2x

=1/e^2integral lim x=0 to infinity4/(2sinxcosx)^2

=4/e^2integral lim x=0 to infinity dx/sin^2(2x)

=4/e^2 integral lim x=0 to infinity cosec^2(2x) dx

=4/e^2 [(-cot2x)/2] x=0 to infinity

=2/e^2[-cot infinity+ cot0]
=infinite

Thanks & Regards

Rinkoo Gupta

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Integration from 0 to infinity x² / (xsinx ecosx)²